How to create Light smear in blender animation
The glow can be created by using a glare node in the compositor.  Since the second accomplishes most of what you want, here's an example:
I created a simple sphere and give it two materials, a shiny dark blue, and a white emission:

dark blue shader:

emission shader:

This is all basic stuff, of course.  Next I rendered the image with F12 and then I went to the Compositing work space and created the glow:

The result looks like this:

You can control the strength and size of the fog flow of course.